Chapter 1: Q3. (page 49)
List and define the four elements of a descriptive statistics problem.
Sample size, variables required, numerical summary tools, and conclusions are the four elements of a descriptive statistics problem.
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Bank corporate mergers. Corporate merger is a means through which one firm (the bidder) acquires control of the assets of another firm (the target). Recently, there was a frenzy of bank mergers in the United States, as the banking industry consolidated into more efficient and more competitive units.
a. Construct a brief questionnaire (two or three questions) that could be used to query a sample of bank presidents concerning their opinions of why the industry is consolidating and whether it will consolidate further.
b. Describe the population about which inferences could be made from the results of the survey.
c. Discuss the pros and cons of sending the questionnaire to all bank presidents versus a sample of 200.
Drafting NFL quarterbacks. The National Football League (NFL) is a lucrative business, generating an annual revenue of about $8 million. One key to becoming a financially successful NFL team is drafting a good quarterback (QB) out of college. The NFL draft allows the worst-performing teams in the previous year the opportunity of selecting the best quarterbacks coming out of college. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful NFL teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted between 1970 and 2007. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11 and 50, or selected after pick 50), NFL winning ratio (percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position is only weakly related to a quarterback’s performance in the NFL. They concluded that “quarterbacks taken higher [in the draft] do not appear to perform any better.”
a. What is the experimental unit for this study?
b. Identify the type (quantitative or qualitative) of each variable measured.
c. Suppose you want to use this study to project the performance of future NFL QBs. Is this an application of descriptive or inferential statistics? Explain.
Treasury deficit prior to the Civil War. In Civil War History (June 2009), historian Jane Flaherty researched the condition of the U.S. Treasury on the eve of the Civil War in 1861. Between 1854 and 1857 (under President Franklin Pierce), the annual surplus/deficit was +18.8, +6.7, +5.3, and +1.3 million dollars, respectively. In contrast, between 1858 and 1861 (under President James Buchanan), the annual surplus/deficit was -27.3, -16.2, -7.2, and -25.2 million dollars, respectively. Flaherty used these data to aid in portraying the exhausted condition of the U.S. Treasury when Abraham Lincoln took office in 1861. Does this study represent a descriptive or inferential statistical study? Explain.
Suppose you have to sort sample units into categories according to their region of origin. The regions are “Africa,” “Americas,” “Asia,” “Europe,” and “Oceania.” For further analysis with a statistical software, you replace each region name with a numerical code: 1 for Africa, 2 for Americas, and so on. Are the data consisting of the region names qualitative or quantitative? Are the numerical codes qualitative or quantitative? Explain your answer.
Define statistical thinking.
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